• Title/Summary/Keyword: Boundary controllability

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BOUNDARY CONTROLLABILITY OF ABSTRACT INTEGRODIFFERENTIAL SYSTEMS

  • Balachandran, K.;Leelamani, A.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.7 no.1
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    • pp.33-45
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    • 2003
  • In this paper we establish a set of sufficient conditions for the boundary controllability of nonlinear integrodifferential systems and Sobolev type integrodifferential systems in Banach spaces by using fixed point theorems.

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Boundary Controllability of Delay Integrodifferential Systems in Banach Spaces

  • Balachandran, K.;Anandhi, E.R.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.4 no.2
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    • pp.67-75
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    • 2000
  • Sufficient conditions for boundary controllability of time varying delay integrodifferential systems in Banach spaces are established. The results are obtained by using the strongly continuous semigroup theory and the Banach contraction principle.

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BOUNDARY CONTROLLABILITY OF SEMILINEAR SYSTEMS IN BANACH SPACES

  • BALACHANDRAN, K.;ANANDHI, E.R.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.5 no.2
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    • pp.149-156
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    • 2001
  • Sufficient conditions for boundary controllability of semilinear systems in Banach spaces are established. The results are obtained by using the analytic semigroup theory and the Banach contraction principle. An example is provided to illustrate the theory.

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CONTROLLABILITY OF NONLINEAR DELAY PARABOLIC EQUATIONS UNDER BOUNDARY CONTROL

  • Park, Jong-Yeoul;Kwun, Young-Chel;Jeong, Jin-Mun
    • Journal of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.333-346
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    • 1996
  • Let $A(\zeta, \partial)$ be a second order uniformly elliptic operator $$ A(\zeta, \partial )u = -\sum_{j, k = 1}^{n} \frac{\partial\zeta_i}{\partial}(a_{jk}(\zeta)\frac{\partial\zeta_k}{\partial u}) + \sum_{j = 1}^{n}b_j(\zeta)\frac{\partial\zeta_j}{\partial u} + c(\zeta)u $$ with real, smooth coefficients $a_{j, k}, b_j$, c defined on $\zeta \in \Omega, \Omega$ a bounded domain in $R^n$ with a sufficiently smooth boundary $\Gamma$.

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ON CONTROLLABILITY FOR FRACTIONAL VOLTERRA-FREDHOLM SYSTEM

  • Ahmed A. Hamoud;Saif Aldeen M. Jameel;Nedal M. Mohammed;Homan Emadifar;Foroud Parvaneh;Masoumeh Khademi
    • Nonlinear Functional Analysis and Applications
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    • v.28 no.2
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    • pp.407-420
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    • 2023
  • In this manuscript, we study the sufficient conditions for controllability of Volterra-Fredholm type fractional integro-differential systems in a Banach space. Fractional calculus and the fixed point theorem are used to derive the findings. Some examples are provided to illustrate the obtained results.

A Class of Singular Quadratic Control Problem With Nonstandard Boundary Conditions

  • Lee, Sung J.
    • Honam Mathematical Journal
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    • v.8 no.1
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    • pp.21-49
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    • 1986
  • A class of singular quadratic control problem is considered. The state is governed by a higher order system of ordinary linear differential equations and very general nonstandard boundary conditions. These conditions in many important cases reduce to standard boundary conditions and because of the conditions the usual controllability condition is not needed. In the special case where the coefficient matrix of the control variable in the cost functional is a time-independent singular matrix, the corresponding optimal control law as well as the optimal controller are computed. The method of investigation is based on the theory of least-squares solutions of multi-valued operator equations.

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APPROXIMATE CONTROLLABILITY FOR NONLINEAR INTEGRODIFFERENTIAL EQUATIONS

  • Choi, J.R.;Kwun, Y.C.;Sung, Y.K.
    • The Pure and Applied Mathematics
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    • v.2 no.2
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    • pp.173-181
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    • 1995
  • Our objective is to investigate approximate controllability of a class of partial integrodifferential systems. This work continuous the investigations of [8]. As a model for this class one may take the equation $\frac{\partialy(t,\;\xi)}{\partialt}\;=\;\frac{\partial}{\partial\xi}(a(t,\;\xi\frac{\partialy(t,\;\xi)}{\partial\xi})\;+\;F(t,\;y(t\;-\;r,\;\xi),\;{{\int_0}^t}\;k(t,\;s,\;y(s\;-\;r,\;\xi))ds)\;+\;b(\xi)u(t),\;0\;\leq\;\xi\;\leq\;1,\;\leq\;t\;\leq\;T$ with initial-boundary conditions y(t,\;0)\;=\;y(t,\;1)\;=\;0,\;0\;\leq\;t\;\leq\;T,\;y(t,\;\xi)\;=\;\phi(t,\;\xi),\;0\;\leq\;1,\;-r\;\leq\;t\;\leq\;0$.(omitted)

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